Lower bounds for asynchronous protocols with high-probability termination

Prove whether the communication lower bounds established for terminating asynchronous protocols extend to protocols that terminate with high probability but not with probability one.

Background

The asynchronous lower bounds in the paper assume termination with probability one. The authors identify protocols that terminate only with high probability as a separate class whose communication complexity is not analyzed.

Extending the lower-bound arguments would require controlling executions in which the relevant parties or party sets terminate, conditioning the input distribution on those executions, and accounting for the resulting loss of input entropy. The paper conjectures that the existing asynchronous lower bounds continue to hold under this weaker termination requirement.

References

Another class of protocols which merit attention are asynchronous protocols that terminate with high probability, but not probability $1$. While we chose not to formalize these protocols to avoid greatly complicating the math, we conjecture that our lower bounds for asynchronous protocols generalize to them.

— Multivalued Consensus: General Adversaries Require More Communication  (2608.17998 - Mizrahi et al., 18 Aug 2026) in Discussion, subsection “Termination with High Probability”